34435 ÷ 3 = 11478 R1
Alright, let's work through the division of 34435 by 3 step by step.

Step 1:
3 goes into 3 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 3 from 3 to get 0.
Bring next digit (4) of the dividend behind the 0 and repeat the process: 4 / 3

Step 2:
3 goes into 4 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 11
Subtract 3 from 4 to get 1.
Bring next digit (4) of the dividend behind the 1 and repeat the process: 14 / 3

Step 3:
3 goes into 14 4 times with a remainder of 2.
Write down 4 as next digit of of the result. 
Result so far: 114
Subtract 12 from 14 to get 2.
Bring next digit (3) of the dividend behind the 2 and repeat the process: 23 / 3

Step 4:
3 goes into 23 7 times with a remainder of 2.
Write down 7 as next digit of of the result. 
Result so far: 1147
Subtract 21 from 23 to get 2.
Bring next digit (5) of the dividend behind the 2 and repeat the process: 25 / 3

Step 5:
3 goes into 25 8 times with a remainder of 1.
Write down 8 as next digit of of the result. 
Result so far: 11478
Subtract 24 from 25 to get 1.

The final result is 11478 with a remainder of 1.